ISSN:0002-9505    

DOI:10.1119/1.18271

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.18275

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.18267

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.18143

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.18145

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.18146

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.18148

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem‐solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.

ISSN:0002-9505    

DOI:10.1119/1.18149

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

At sea, on a windless day, in a strong swell, free floating ships will roll heavily. It was believed in the days of the clipper ships that under those circumstances two vessels at close distance will attract each other. Do they? The ships are harmonic oscillators in a wave field and as such analogous to two atoms in the sea of vacuum fluctuations. These atoms do attract: the van der Waals force.

ISSN:0002-9505    

DOI:10.1119/1.18150

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

In ‘‘Two New Sciences’’ (TNS) Galileo presents a number of theorems and propositions for smooth solid spheres released from rest and rolling a distancedin timetdown an incline of heightHand lengthL. We collect and summarize his results in a single grand proportionalityP:d1/d2=(t21/t22)(H/L)1/(H/L)2. (P) From what he writes in TNS it is clear that what we callPis assumed by Galileo to hold for all inclinations including vertical free fall withH/L=1. But in TNS he describes only experiments withgentleinclinationsH/L<1/2. Indeed he cannot have performed the vertical free fall (H=L) experiment, because we (moderns) know that as we increaseH/L,Pstarts to break down whenH/Lexceeds about 0.5, because the sphere, which rolls without slipping for smallH/L, starts to slip, whencedstarts to exceed the predictions ofP, becoming too large by a factor of 7/5 for vertical free fall atH/L=1. In 1973 Drake and in 1975 Drake and MacLachlan published their analysis of a previously unpublished experiment that Galileo performed that (without his realizing it) directly compared rolling without slipping to free fall. In the experiment, a sphere that has gained speedv1while rolling down a gentle incline is deflected so as to be launched horizontally with speedv1into a free fall orbit discovered by Galileo to be a parabola. The measured horizontal distanceX2traveled in this parabolic orbit (for a given vertical distance fallen to the floor) was smaller than he expected, by a factor 0.84. But that is exactly what we (moderns) expect, since we know that Galileo did not appreciate the difference between rolling without slipping, and slipping on a frictionless surface. We therefore expect him to predictX2too large by a factor (7/5)1/2=1/0.84. He must have been puzzled. Easy ‘‘home experiments’’ with simple apparatus available to Galileo (no frictionless air tracks, strobe lamps, or electronic timers!) allow the student to use his/her musical ear (for rhythm and tempo) to study vertical free fall as well as balls rolling down steep or gentle inclines, with or without slipping, and perhaps appreciate Galileo’s dilemma.

ISSN:0002-9505    

DOI:10.1119/1.18151

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP